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A SAT Solver and Computer Algebra Attack on the Minimum Kochen-Specker Problem (2306.13319v7)
Published 23 Jun 2023 in quant-ph, cs.CC, and math.CO
Abstract: One of the fundamental results in quantum foundations is the Kochen-Specker (KS) theorem, which states that any theory whose predictions agree with quantum mechanics must be contextual, i.e., a quantum observation cannot be understood as revealing a pre-existing value. The theorem hinges on the existence of a mathematical object called a KS vector system. While many KS vector systems are known, the problem of finding the minimum KS vector system in three dimensions (3D) has remained stubbornly open for over 55 years. To address the minimum KS problem, we present a new verifiable proof-producing method based on a combination of a Boolean satisfiability (SAT) solver and a computer algebra system (CAS) that uses an isomorph-free orderly generation technique that is very effective in pruning away large parts of the search space. Our method shows that a KS system in 3D must contain at least 24 vectors. We show that our sequential and parallel Cube-and-Conquer (CnC) SAT+CAS methods are significantly faster than SAT-only, CAS-only, and a prior CAS-based method of Uijlen and Westerbaan. Further, while our parallel pipeline is somewhat slower than the parallel CnC version of the recently introduced Satisfiability Modulo Theories (SMS) method, this is in part due to the overhead of proof generation. Finally, we provide the first computer-verifiable proof certificate of a lower bound to the KS problem with a size of 40.3 TiB in order 23.
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Main Track, to appear (2023). https://doi.org/10.48550/arXiv.2306.10427 Pavičić [2017] Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Uijlen, S., Westerbaan, B.: A Kochen-Specker system has at least 22 vectors. New Generation Computing 34(1), 3–23 (2016) https://doi.org/10.1007/s00354-016-0202-5 Kirchweger et al. [2023] Kirchweger, M., Peitl, T., Szeider, S.: Co-Certificate Learning with SAT Modulo Symmetries. International Joint Conferences on Artificial Intelligence Organization, California. Main Track, to appear (2023). https://doi.org/10.48550/arXiv.2306.10427 Pavičić [2017] Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Peitl, T., Szeider, S.: Co-Certificate Learning with SAT Modulo Symmetries. International Joint Conferences on Artificial Intelligence Organization, California. Main Track, to appear (2023). https://doi.org/10.48550/arXiv.2306.10427 Pavičić [2017] Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. 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[2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. 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[2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Uijlen, S., Westerbaan, B.: A Kochen-Specker system has at least 22 vectors. New Generation Computing 34(1), 3–23 (2016) https://doi.org/10.1007/s00354-016-0202-5 Kirchweger et al. [2023] Kirchweger, M., Peitl, T., Szeider, S.: Co-Certificate Learning with SAT Modulo Symmetries. International Joint Conferences on Artificial Intelligence Organization, California. Main Track, to appear (2023). https://doi.org/10.48550/arXiv.2306.10427 Pavičić [2017] Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. 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[2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Peitl, T., Szeider, S.: Co-Certificate Learning with SAT Modulo Symmetries. International Joint Conferences on Artificial Intelligence Organization, California. Main Track, to appear (2023). https://doi.org/10.48550/arXiv.2306.10427 Pavičić [2017] Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. 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A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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[2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. 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[2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. 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AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Uijlen, S., Westerbaan, B.: A Kochen-Specker system has at least 22 vectors. New Generation Computing 34(1), 3–23 (2016) https://doi.org/10.1007/s00354-016-0202-5 Kirchweger et al. [2023] Kirchweger, M., Peitl, T., Szeider, S.: Co-Certificate Learning with SAT Modulo Symmetries. International Joint Conferences on Artificial Intelligence Organization, California. Main Track, to appear (2023). https://doi.org/10.48550/arXiv.2306.10427 Pavičić [2017] Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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Main Track, to appear (2023). https://doi.org/10.48550/arXiv.2306.10427 Pavičić [2017] Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Uijlen, S., Westerbaan, B.: A Kochen-Specker system has at least 22 vectors. New Generation Computing 34(1), 3–23 (2016) https://doi.org/10.1007/s00354-016-0202-5 Kirchweger et al. [2023] Kirchweger, M., Peitl, T., Szeider, S.: Co-Certificate Learning with SAT Modulo Symmetries. International Joint Conferences on Artificial Intelligence Organization, California. Main Track, to appear (2023). https://doi.org/10.48550/arXiv.2306.10427 Pavičić [2017] Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Uijlen, S., Westerbaan, B.: A Kochen-Specker system has at least 22 vectors. New Generation Computing 34(1), 3–23 (2016) https://doi.org/10.1007/s00354-016-0202-5 Kirchweger et al. [2023] Kirchweger, M., Peitl, T., Szeider, S.: Co-Certificate Learning with SAT Modulo Symmetries. International Joint Conferences on Artificial Intelligence Organization, California. Main Track, to appear (2023). https://doi.org/10.48550/arXiv.2306.10427 Pavičić [2017] Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. 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[2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. 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[2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). 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[2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. 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[2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. 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[2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Peitl, T., Szeider, S.: Co-Certificate Learning with SAT Modulo Symmetries. International Joint Conferences on Artificial Intelligence Organization, California. Main Track, to appear (2023). https://doi.org/10.48550/arXiv.2306.10427 Pavičić [2017] Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. 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[2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. 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[2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. 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Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. 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[2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). 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[2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. 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[2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. 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[2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. 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[2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). 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[2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. 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[2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. 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[2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. 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[2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. 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[2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Uijlen, S., Westerbaan, B.: A Kochen-Specker system has at least 22 vectors. New Generation Computing 34(1), 3–23 (2016) https://doi.org/10.1007/s00354-016-0202-5 Kirchweger et al. [2023] Kirchweger, M., Peitl, T., Szeider, S.: Co-Certificate Learning with SAT Modulo Symmetries. International Joint Conferences on Artificial Intelligence Organization, California. Main Track, to appear (2023). https://doi.org/10.48550/arXiv.2306.10427 Pavičić [2017] Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. 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Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. 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[2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets. Physical Review A 95(6), 062121 (2017) Budroni et al. [2022] Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. 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[2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., Larsson, J.-Å.: Kochen-specker contextuality. Reviews of Modern Physics 94(4), 045007 (2022) Held [2009] Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. 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Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. 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In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. 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Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Held, C.: Kochen–Specker theorem. In: Compendium of Quantum Physics, pp. 331–335. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-70626-7_104 Pavičić [2019] Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Hypergraph contextuality. Entropy 21(11), 1107 (2019) Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. 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[2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. 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AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577 (2005) Pavičić [2023] Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M.: Quantum contextuality. Quantum 7, 953 (2023) Peres [1991] Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. 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[2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Peres, A.: Two simple proofs of the Kochen–Specker theorem. Journal of Physics A: Mathematical and General 24(4), 175–178 (1991) https://doi.org/10.1088/0305-4470/24/4/003 Pavicic and Megill [2022] Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavicic, M., Megill, N.D.: Automated generation of arbitrarily many Kochen-Specker and other contextual sets in odd-dimensional Hilbert spaces. Phys. Rev. A 106(6), 060203–1 (2022) https://doi.org/10.1103/PhysRevA.106.L060203 arXiv:2202.08197 [quant-ph] Biere et al. [2021] Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. 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[2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. 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In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Heule, M., Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2021). https://doi.org/10.3233/faia336 Ganesh and Vardi [2020] Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ganesh, V., Vardi, M.Y.: On the Unreasonable Effectiveness of SAT Solvers. Cambridge University Press, Cambridge (2020). https://doi.org/10.1017/9781108637435.032 Metin et al. [2018] Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Metin, H., Baarir, S., Colange, M., Kordon, F.: CDCLSym: Introducing Effective Symmetry Breaking in SAT Solving. Springer, New York (2018). https://doi.org/10.1007/978-3-319-89960-2_6 Bright et al. [2022] Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: When satisfiability solving meets symbolic computation. Communications of the ACM 65(7), 64–72 (2022) https://doi.org/10.1145/3500921 Aloul et al. [2003] Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient Symmetry Breaking for Boolean Satisfiability. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2003). https://dl.acm.org/doi/10.5555/1630659.1630699 Barrett et al. [2016] Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). 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Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016) Zulkoski et al. [2015] Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zulkoski, E., Ganesh, V., Czarnecki, K.: MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_41 Ábrahám [2015] Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Ábrahám, E.: Building bridges between symbolic computation and satisfiability checking (2015). https://doi.org/10.1145/2755996.2756636 Kaufmann and Biere [2023] Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
- Kaufmann, D., Biere, A.: Improving AMulet2 for verifying multiplier circuits using SAT solving and computer algebra. International Journal on Software Tools for Technology Transfer (2023) https://doi.org/10.1007/s10009-022-00688-6 Mahzoon et al. [2022] Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. 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[2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Scholl, C., Konrad, A., Drechsler, R.: Formal verification of modular multipliers using symbolic computer algebra and boolean satisfiability. In: Proceedings of the 59th ACM/IEEE Design Automation Conference. ACM, New York (2022). https://doi.org/10.1145/3489517.3530605 Mahzoon et al. [2018] Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Mahzoon, A., Große, D., Drechsler, R.: Combining symbolic computer algebra and boolean satisfiability for automatic debugging and fixing of complex multipliers. In: 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 351–356 (2018). https://doi.org/10.1109/ISVLSI.2018.00071 Heule et al. [2021] Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
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(eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kauers, M., Seidl, M.: New ways to multiply 3×3333\times 33 × 3-matrices. Journal of Symbolic Computation 104, 899–916 (2021) https://doi.org/10.1016/j.jsc.2020.10.003 Neiman et al. [2022] Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Neiman, D., Mackey, J., Heule, M.: Tighter bounds on directed Ramsey number R(7)𝑅7R(7)italic_R ( 7 ). Graphs and Combinatorics 38(5) (2022) https://doi.org/10.1007/s00373-022-02560-5 Bright et al. [2016] Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Ganesh, V., Heinle, A., Kotsireas, I., Nejati, S., Czarnecki, K.: MathCheck2: A SAT+CAS verifier for combinatorial conjectures (2016). https://doi.org/10.1007/978-3-319-45641-6_9 England [2022] England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) England, M.: SC-Square: Overview to 2021. In: Bright, C., Davenport, J. (eds.) Proceedings of the 6th SC-Square Workshop, pp. 1–6 (2022). https://ceur-ws.org/Vol-3273/invited1.pdf Jost [1976] Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jost, R.: Measures on the finite dimensional subspaces of a Hilbert space: remarks to a theorem by A. M. Gleason. Studies in Mathematical Physics: Essays in Honour of Valentine Bergmann, 209–228 (1976) https://doi.org/10.1515/9781400868940-011 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. 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[2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. 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- Li, Z., Bright, C., Ganesh, V.: An sc-square approach to the minimum kochen-specker problem. In: Uncu, A.K., Barbosa, H. (eds.) Proceedings of the 7th SC-Square Workshop Co-located with the Federated Logic Conference, SC-Square@FLoC 2022, as a Part of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, Haifa, Israel, August 12, 2022. CEUR Workshop Proceedings, vol. 3458, pp. 55–66. CEUR-WS.org, ??? (2022). https://ceur-ws.org/Vol-3458/paper6.pdf Zhengyu Li [2024] Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Zhengyu Li, V.G. Curtis Bright: A sat solver and computer algebra attack on the minimum kochen-specker problem. In: Proceedings of the AAAI Conference on Artificial Intelligence (2024) Bright et al. [2021] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: A SAT-based Resolution of Lam’s Problem. AAAI Press, California USA (2021). https://doi.org/10.1609/aaai.v35i5.16483 Junttila et al. [2020] Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Junttila, T., Karppa, M., Kaski, P., Kohonen, J.: An adaptive prefix-assignment technique for symmetry reduction. Journal of Symbolic Computation 99, 21–49 (2020) https://doi.org/10.1016/j.jsc.2019.03.002 Savela et al. [2020] Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Savela, J., Oikarinen, E., Järvisalo, M.: Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation. EasyChair, UK (2020). https://doi.org/10.29007/k8jd Crawford et al. [1996] Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning. KR’96, pp. 148–159. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996). https://dl.acm.org/doi/10.5555/3087368.3087386 Heule [2019] Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H.: Optimal symmetry breaking for graph problems. Mathematics in Computer Science 13(4), 533–548 (2019) https://doi.org/10.1007/s11786-019-00397-5 Sellmann and Hentenryck [2005] Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. 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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. 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AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Sellmann, M., Hentenryck, P.V.: Structural Symmetry Breaking. Professional Book Center, California (2005). http://ijcai.org/Proceedings/05/Papers/1121.pdf Kirchweger and Szeider [2021] Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Szeider, S.: SAT Modulo Symmetries for Graph Generation. Schloss Dagstuhl, Dagstuhl, Germany (2021). https://doi.org/10.4230/LIPIcs.CP.2021.34 Kirchweger et al. [2022] Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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[2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. 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[2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. 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[2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
- Kirchweger, M., Scheucher, M., Szeider, S.: A SAT Attack on Rota’s Basis Conjecture. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPICS.SAT.2022.4 Bright et al. [2020] Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. 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Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Kotsireas, I., Ganesh, V.: Applying computer algebra systems with SAT solvers to the Williamson conjecture. Journal of Symbolic Computation 100, 187–209 (2020) https://doi.org/10.1016/j.jsc.2019.07.024 Gerlach and Stern [1922] Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
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[2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Gerlach, W., Stern, O.: Der experimentelle nachweis der richtungsquantelung im magnetfeld. Zeitschrift für Physik 9, 349–352 (1922) https://doi.org/10.1007/BF01326983 Huang et al. [2003] Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Huang, Y.-F., Li, C.-F., Zhang, Y.-S., Pan, J.-W., Guo, G.-C.: Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters 90(25) (2003) https://doi.org/10.1103/physrevlett.90.250401 Pavičić et al. [2005] Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. 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Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
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In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Pavičić, M., Merlet, J.-P., McKay, B., Megill, N.D.: Kochen–Specker vectors. Journal of Physics A: Mathematical and General 38(7), 1577–1592 (2005) https://doi.org/10.1088/0305-4470/38/7/013 Heule et al. [2011] Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. 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In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
- Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: Guiding CDCL SAT solvers by lookaheads (2011). https://doi.org/10.1007/978-3-642-34188-5_8 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. 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University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
- Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Heule [2018] Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.: Schur number five. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32. AAAI Press, California (2018). https://doi.org/10.1609/aaai.v32i1.12209 McKay and Piperno [2014] McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) McKay, B.D., Piperno, A.: Practical graph isomorphism, II. Journal of Symbolic Computation 60, 94–112 (2014) https://doi.org/10.1016/j.jsc.2013.09.003 Lisoněk et al. [2014] Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. 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Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. 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[2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. 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[2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
- Lisoněk, P., Badzia̧g, P., Portillo, J.R., Cabello, A.: Kochen-Specker set with seven contexts. Physical Review A 89(4) (2014) https://doi.org/10.1103/physreva.89.042101 Codish et al. [2019] Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Constraints for symmetry breaking in graph representation. Constraints 24(1), 1–24 (2019) https://doi.org/10.1007/s10601-018-9294-5 Knuth [2015] Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. 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[2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. 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Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 6: Satisfiability. Addison-Wesley Professional, Massachusetts (2015). https://dl.acm.org/doi/abs/10.5555/2898950 Read [1978] Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Elsevier, Amsterdam (1978). https://doi.org/10.1016/S0167-5060(08)70325-X Faradžev [1978] Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Faradžev, I.A.: Constructive enumeration of combinatorial objects (1978) Biere et al. [2020] Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. 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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. 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[2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
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[2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. 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Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
- Biere, A., Fazekas, K., Fleury, M., Heisinger, M.: CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling Entering the SAT Competition 2020. University of Helsinki, Helsinki (2020). http://hdl.handle.net/10138/318754 Liang et al. [2016] Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
- Liang, J.H., Ganesh, V., Poupart, P., Czarnecki, K.: Learning Rate Based Branching Heuristic for SAT Solvers (2016). https://doi.org/10.1007/978-3-319-40970-2_9 de Moura and Bjørner [2008] de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) de Moura, L., Bjørner, N.: Z3: An efficient SMT solver (2008). https://doi.org/10.1007/978-3-540-78800-3_24 Jovanović and de Moura [2012] Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jovanović, D., de Moura, L.: Solving non-linear arithmetic (2012). https://doi.org/10.1007/978-3-642-31365-3_27 Heule et al. [2017] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. In: IJCAI, vol. 17, pp. 228–245 (2017). https://doi.org/10.24963/ijcai.2017/683 Heule et al. [2016] Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. 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[2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. 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[2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
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In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving very hard problems: Cube-and-conquer, a hybrid SAT solving method. 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[2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
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- Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean Pythagorean triples problem via cube-and-conquer. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 228–245. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_15 Jha et al. [2024] Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
- Jha, P., Li, Z., Lu, Z., Bright, C., Ganesh, V.: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT Solver for Hard Combinatorial Problems. arXiv preprint arXiv:2401.13770 (2024) Wetzler et al. [2014] Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
- Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In: Lecture Notes in Computer Science vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31 Bright et al. [2020] Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Bright, C., Cheung, K.K.H., Stevens, B., Kotsireas, I., Ganesh, V.: Nonexistence certificates for ovals in a projective plane of order ten. In: Lecture Notes in Computer Science vol. 12126, pp. 97–111. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_8 Hagberg et al. [2008] Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring Network Structure, Dynamics, and Function using NetworkX, Pasadena, CA USA (2008). https://www.osti.gov/biblio/960616 Li et al. [2022] Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022) Li, Z., Bright, C., Ganesh, V.: A SAT Solver + Computer Algebra Attack on the Minimum Kochen–Specker Problem. Technical report, https://cs.curtisbright.com/reports/nmi-ks-preprint.pdf (2022)
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